{"as_of":"2026-08-22T00:42:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:042e48821ab44f769787a9fed48fd2f8dac36342b66d1c38efa95d70044bbb25","coverage":[{"denominator":34,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":34,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T23:59:14.986615Z","state":"measured"},{"denominator":34,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":34,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-21T06:32:19.484+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2509.06260/citation-record","integrity":"/paper/2509.06260/integrity","json":"/paper/2509.06260/citation-record.json","paper":"/paper/2509.06260"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4007/annals.2021","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:17.029953Z","title":"Marginal triviality of the scaling limits of critical 4D Ising andϕ 4 4 models.Ann","venue":null,"work_id":"e9643594-2020-4745-86e8-8fbb2cc5d80e","year":2021},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:11.941799Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:98402b6b82d24ab51b9e455b08e0d41710ef25f430dbdb1c779ad060b58b4bc0","observation_id":"edc2cc4b-403b-4d48-9594-dac945d0ad9a","resolution":{"observed_at":"2026-08-04T23:59:17.126031Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:12.006053Z","title":"The two-dimensional stochastic heat equation: renor- malizing a multiplicative noise.J","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:12.006053Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:835155ee6192a1180043541cfcb526e474c1b4610d4b671aecd3161ed460795a","observation_id":"03c25985-2ecf-4783-8fe7-16f25da00eca","resolution":{"observed_at":"2026-08-04T23:59:12.006053Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0378-4371(93)90338-5","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Physica A Statistical Mechanics and its Applications","work_id":"3e48b654-e671-4376-af88-900ce3ccf086","year":1993},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:12.122565Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:84a7b1afaa58a7f3474019ef62faddf1db5974d59cc2782f1d979fc3e4cd9e0c","observation_id":"44645b9d-c0e5-496b-8c50-75ebd61760a7","resolution":{"observed_at":"2026-08-04T23:59:16.958060Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:12.194525Z","title":"2D anisotropic KPZ at station- arity: scaling, tightness and nontriviality.Ann","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:12.194525Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:8456db0abadbf179a653958180fe59f687c5b2ace8a2990ed6be6c658c99c76d","observation_id":"21c0b646-0ca1-43a1-87ef-72ada9d14c60","resolution":{"observed_at":"2026-08-04T23:59:12.194525Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1215/00127094-2022-0094","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Weak coupling limit of the anisotropic KPZ equation.Duke Math","venue":"Duke Mathematical Journal","work_id":"0d0345c8-b0e6-4836-8bc7-ad891cba4189","year":2023},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:12.296720Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:d974c91df3d719c1a968841a74ceebcf80a4ea68730a864aed65d9673c2fff16","observation_id":"9e837f10-0442-43d4-8df2-99598503e805","resolution":{"observed_at":"2026-08-04T23:59:16.764979Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-07T00:08:29.374757+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-07T00:08:29.374757+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00220-024-04966-z","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Gaussian fluctuations for the stochastic Burgers equation in dimensiond≥2.Comm","venue":"Communications in Mathematical Physics","work_id":"2328a9ff-2c8a-4abe-9332-b6902bd9a46e","year":2024},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:12.396925Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:0984ab1da60634a2cbc0b2bd062a70b06780dc0e32f03bb51a2551d108faac79","observation_id":"12f2510e-d49c-4bcf-b2c6-266d4663b349","resolution":{"observed_at":"2026-08-04T23:59:16.641822Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:12.513061Z","title":"The critical 2dstochastic heat flow is not a Gaussian multiplicative chaos.Ann","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:12.513061Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:a44c17e961dbcab36a6ea156eb88aa4da7c43ccf042ee10af5bdf1b453d733c4","observation_id":"b702a05a-0fba-4063-b821-85e2ef21cb46","resolution":{"observed_at":"2026-08-04T23:59:12.513061Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:12.627708Z","title":"The critical 2d stochastic heat flow.Invent","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:12.627708Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:28e98ae9060437c85cf50a634c5dfa774f1c84e5aaeb1b89a8ad7c7f1f2eb4f7","observation_id":"9bd99ef6-b670-400b-bab0-41584cace572","resolution":{"observed_at":"2026-08-04T23:59:12.627708Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:17.498713Z","title":"The two-dimensional KPZ equation in the entire subcritical regime.Ann","venue":null,"work_id":"40cccfd3-aa16-4ea4-88fb-bd9b3c0b2a52","year":2020},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:12.727631Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:6b4888e25cf1a513adccb312a50e54f837c2d44aad7910022df025bf4e2056e1","observation_id":"e57150c2-8956-4801-84e6-d46f6f181cc4","resolution":{"observed_at":"2026-08-04T23:59:17.502511Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1214/17-aap1276","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Universality in marginally relevant disordered systems.Ann","venue":"The Annals of Applied Probability","work_id":"dd16d78f-9b87-4cd3-b33c-4eced8fd8791","year":2017},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:12.797839Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:5497f1c99469a5f099ad01f93c63b53e2e0b25da33e64b93a05a85d41ce67a44","observation_id":"d8caa4fc-68aa-4a3c-96d1-bf3c52a39d17","resolution":{"observed_at":"2026-08-04T23:59:16.506295Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1214/19-aop1382","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Constructing a solution of the (2 + 1)-dimensional KPZ equation.Ann","venue":"The Annals of Probability","work_id":"1640a8d8-5c92-4175-8a43-180609c512f7","year":2020},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:12.930578Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:fa07f876404a883dd968c273ba8e4ccb6edc52de3868d6560ebe3569e90b4736","observation_id":"473b2072-c359-4d9f-8d4c-797c3d2d7f8c","resolution":{"observed_at":"2026-08-04T23:59:16.332895Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:13.076712Z","title":"Central limit theorems for spatial averages of the stochastic heat equation via Malliavin-Stein’s method.Stoch","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:13.076712Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:d7a13e4f5b902af857d5261e4b6f9a675c0d6c6e877b6f587582ba403ec7823f","observation_id":"f759652f-b9c2-40ef-b431-93fc7de19eae","resolution":{"observed_at":"2026-08-04T23:59:13.076712Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2205.14488","last_updated":"2024-12-12T18:34:57Z","snapshot_observed_at":"2026-08-16T16:56:57.357382Z","submitted_at":"2022-05-28T17:41:11Z","title":"Norm inflation for the cubic nonlinear heat equation above the scaling critical regularity","version":2},"cited_work":{"arxiv_id":"2205.14488","doi":null,"metadata_source":"pith","pith_arxiv_id":"2205.14488","snapshot_observed_at":"2026-08-04T23:59:17.423885Z","title":"Norm inflation for the cubic nonlinear heat equation above the scaling critical regularity","venue":"math.AP","work_id":"131e95b1-a773-44db-8572-c15dfdaf93d7","year":2022},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:13.217700Z"},"links":{"cited_paper":"/paper/2205.14488","citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:54ebcb904ba4a7928129ab942e8261c8a57c9d553f43d0c8abc2a8f357aa80e5","observation_id":"dbc40ad9-4a8b-43b5-a5da-aa3ae3753fd5","resolution":{"observed_at":"2026-08-04T23:59:17.427654Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.16056","last_updated":"2025-07-21T20:46:41Z","snapshot_observed_at":"2026-08-20T00:59:05.963385Z","submitted_at":"2025-07-21T20:46:41Z","title":"Conditional GMC within the stochastic heat flow","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.16056","snapshot_observed_at":"2026-08-04T23:59:13.350794Z","title":"Conditional GMC within the stochastic heat flow, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:13.350794Z"},"links":{"cited_paper":"/paper/2507.16056","citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:69410222e8064199b263ff22bf4ba81126f0dcb8b9ab8982d73fe6158b6f21f6","observation_id":"0db1c7fb-808a-4228-997f-fb61758ec54a","resolution":{"observed_at":"2026-08-04T23:59:13.350794Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00220-021-04149-0","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Weak-disorder limit at criticality for directed polymers on hierarchical graphs.Comm","venue":"Communications in Mathematical Physics","work_id":"1257a982-4f7e-4a1c-8d63-938cac3f13ae","year":2021},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:13.410228Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:d594e251c342a073c6bed04ed77054e956a9e915bb5c3365ba5c953c4f08c753","observation_id":"1f79cbbf-4c2e-40f0-9804-860320f680d9","resolution":{"observed_at":"2026-08-04T23:59:16.116741Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2508.07776","last_updated":"2025-08-11T09:03:43Z","snapshot_observed_at":"2026-08-05T21:55:56.083302Z","submitted_at":"2025-08-11T09:03:43Z","title":"Ergodicity of infinite volume $\\Phi^4_3$ at high temperature","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.07776","snapshot_observed_at":"2026-08-04T23:59:13.494881Z","title":"Ergodicity of infinite volume Φ 4 3 at high temperature, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:13.494881Z"},"links":{"cited_paper":"/paper/2508.07776","citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:79e6d3a45acdbbefd943f588fb15448a398ef9e3db6d637ce0c71e75fc4cac04","observation_id":"f2f7ed70-6b0b-45f2-aeef-5385beb0b4b7","resolution":{"observed_at":"2026-08-04T23:59:13.494881Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.matpur.2023","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:15.847578Z","title":"Non-perturbative approach to the Bourgain-Spencer conjecture in stochastic homogenization.J","venue":null,"work_id":"7ff18c83-59cc-4fdd-886b-dfeb89b0df71","year":2023},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:13.576997Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:a5bbec448f4a974fdd88daccbca8a8a542fa581e403b90867e487f57786bdf8d","observation_id":"e3fa73b1-c8e5-4d43-a33c-02d65b9391f5","resolution":{"observed_at":"2026-08-04T23:59:15.915185Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2308.11850","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:17.388823Z","title":"The 2D nonlinear stochastic heat equation: pointwise statistics and the decoupling function, 2023","venue":null,"work_id":"fc1958d4-d615-4ca1-b88d-d40dfb98cefc","year":2023},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:13.690939Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:1a45b2eb54205ffab642778e5df83388ef9be165d25276bc86770578d1f897a1","observation_id":"5b079898-82e1-45f9-a316-4a1e666b7f0f","resolution":{"observed_at":"2026-08-04T23:59:17.394519Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1214/21-aop1563","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"A forward-backward SDE from the 2D nonlinear stochastic heat equation.Ann","venue":"The Annals of Probability","work_id":"cba78ed2-a5dc-4b86-982b-1959a27085b9","year":2022},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:13.761920Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:bd29bd62ce4cd18b2a1ec1946b52f89b1af2eb28a38ead06d51dad00135558bc","observation_id":"6ff58856-84e4-4e05-a079-aa06c05d2425","resolution":{"observed_at":"2026-08-04T23:59:15.722737Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:17.487072Z","title":"Prentice-Hall, Inc., Engle- wood Cliffs, NJ, 1964, pages xiv+347","venue":null,"work_id":"82756e6a-6ccc-4dfb-b7bc-257a6741ce4d","year":1964},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:13.852922Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:e8d97b94c8d19929f769c4637aa63a467458da47f4c92eda5c212f9abcf7b787","observation_id":"5a4d7721-9d8f-4df1-9782-6b3697902195","resolution":{"observed_at":"2026-08-04T23:59:17.491424Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00440-024-01312-1","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"The Allen–Cahn equation with weakly critical random initial datum.Probability Theory and Related Fields, 192(3-4):1373–1446, 2025.doi: 10.1007/s00440-024-01312-1","venue":"Probability Theory and Related Fields","work_id":"c608befd-d730-4edf-9667-e16c67b25fcb","year":2025},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:13.910601Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:c2bdcc5e608bbfbeb33ff1b75fbee8dbe1118af53c6ade991ea3e6b4d72b2cc3","observation_id":"0fbe154e-d52b-43b4-9f32-266eb12d5ff2","resolution":{"observed_at":"2026-08-04T23:59:15.537939Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s40072-019-00144-8","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Gaussian fluctuations from the 2D KPZ equation.Stoch","venue":"Stochastic Partial Differential Equations Analysis and Computations","work_id":"2a0a4d68-2e8e-4e06-a12a-4db2740804c8","year":2020},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:14.007232Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:eeb19bcef0db925e3d5caca61fef57f4db53466afa40b8f73c544535ee141186","observation_id":"d37bc308-59c2-49f9-8920-608e4aa6fec0","resolution":{"observed_at":"2026-08-04T23:59:15.331427Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:17.476341Z","title":"Stochastic heat flow is a black noise, 2025","venue":null,"work_id":"61a76a11-447a-48cf-806f-0d139db8f9fe","year":2025},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:14.067277Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:ed107a81c6ab1cd61e20b9e198dd23f48c46756846338d1ad5e806fa2fe8d812","observation_id":"1842f8f0-0cc2-4b83-9e37-d3b904fc6be2","resolution":{"observed_at":"2026-08-04T23:59:17.479954Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:17.465343Z","title":"The Allen-Cahn equation with generic initial datum.Probab","venue":null,"work_id":"b72de89c-8ec6-4047-b280-00f3d25c88ad","year":2023},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:14.125083Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:5a0a9ecd6fa3d78208baf395b6f052fec4fb592a844fa225625703a32262e882","observation_id":"369908df-1216-41fa-b563-164df7fc4559","resolution":{"observed_at":"2026-08-04T23:59:17.469262Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1214/ejp.v17-1731","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Ryser, and Hendrik Weber","venue":"Electronic Journal of Probability","work_id":"1d5f448b-caa8-4a90-baf5-847f8d29fa98","year":2012},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:14.210987Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:f96bc25a934bb602fbc69bfa1ed9d4421db526ba00814a5517f1f7f818db465f","observation_id":"2aee0e32-1285-4301-9913-dc4985c9a27a","resolution":{"observed_at":"2026-08-04T23:59:15.168504Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:14.318416Z","title":"Kohn and Felix Otto","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:14.318416Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:d9402eac9e51db0ad25dc66d4040ac0e5b5d1c116f412b917b8194cc4608c6b8","observation_id":"5e85f388-f17b-4d48-81d0-aa30ac676f2e","resolution":{"observed_at":"2026-08-04T23:59:14.318416Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:14.388640Z","title":"Global well-posedness of the dynamic Φ 4 model in the plane.Ann","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:14.388640Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:b669c10d76e5aaf0584a68ff327b8c84b984f2a10a0db79712a23d4a38e35b16","observation_id":"67088286-9470-4b8f-82fc-408c2ee96b77","resolution":{"observed_at":"2026-08-04T23:59:14.388640Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:14.476540Z","title":"Second order Poincar´ e inequalities and CLTs on Wiener space.J","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:14.476540Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:75f4bda513b5b152b86dac8201d8becbf0f38e6b46d2b52f1707798fc0ae9f0f","observation_id":"59954eb5-8513-4580-86c7-c2fc9cd63bec","resolution":{"observed_at":"2026-08-04T23:59:14.476540Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:17.454942Z","title":"Probability and its Applications (New York)","venue":null,"work_id":"5149bfc9-8a76-409c-8d5d-8ca03dc58948","year":2006},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:14.591827Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:aa06d48dc88478468dbb918374992e4bd2a090808c23b5a537e52624d1a5450c","observation_id":"ba760a51-6e86-4f1c-b0d2-e1727f5979d6","resolution":{"observed_at":"2026-08-04T23:59:17.458759Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:14.654995Z","title":"Universal scaling in the motion of random interfaces.Phys","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:14.654995Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:7aa530a312742014f09c1b3f5a952ccabd8007590fab07d4c8977f0aa414af15","observation_id":"5fd80a23-50a1-4b16-b183-c93f7af78ded","resolution":{"observed_at":"2026-08-04T23:59:14.654995Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:17.444984Z","title":"Parisi and Yong Shi Wu","venue":null,"work_id":"24f21190-b7a6-4d5d-9a7c-4063ec66db36","year":1981},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:14.738140Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:7258fa0e27e5f8ba59801af340a927801bad299dc75d410bd15dac7e0a034581","observation_id":"58fda477-cb1a-4644-968a-9fca150493ec","resolution":{"observed_at":"2026-08-04T23:59:17.448388Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:14.851968Z","title":"Stochastic heat flow by moments, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:14.851968Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:f21068ca6dc14cb90322278e2b082fe56c277de14d162b301bcad66ee05a9f44","observation_id":"04a444f4-9080-41f2-98d3-3ead0d3eb5a4","resolution":{"observed_at":"2026-08-04T23:59:14.851968Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:17.434001Z","title":null,"venue":null,"work_id":"12027b73-009d-4451-bf49-0a17f5497114","year":2009},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:14.926362Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:ef3679ca29c980be97c5b6837a438ee452765794662449c9565c8b434f159de8","observation_id":"fce91136-8d55-4638-8238-ba407d186bdc","resolution":{"observed_at":"2026-08-04T23:59:17.437517Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T23:59:14.986615Z","title":"Viens and Andrew B","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-04T23:59:14.986615Z"},"links":{"citing_paper":"/paper/2509.06260"},"observation_digest":"sha256:5de3de84144572912887f9ce176f396e5bb0256d0fde511c8b63affd257117aa","observation_id":"c58cee1b-fac4-473d-ab28-4fcd782f55ee","resolution":{"observed_at":"2026-08-04T23:59:14.986615Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2509.06260","last_updated":"2025-09-08T00:54:51Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-20T00:59:27.391006Z","submitted_at":"2025-09-08T00:54:51Z","title":"McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data"},"reference_resolution":{"displayed":34,"state_counts":{"malformed_identifier":4,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":14,"verified_fuzzy":6},"total_outbound_references":34},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2509.06260."}